Network DAW to another computer but not to internet

I don't know much about networking so I hope this question is clear.

I have two laptops that are connected to the internet and another computer, my DAW, which is off the internet (except when updating Sonar).

I've set up a Homegroup to network the two laptops to each other.
What I'd like to do is connect the DAW (via the Homegroup network) to the laptops, but without exposing the DAW to the internet.
Is there a way to do this? 

disconnecting the router from the outside world is a form of "air gap", and it is easy, and it is effective, and if you have  no need for internet access, or at least no need for internet access while the DAW is connected to the laptop then it will work.
 
There is a far more elegant solution however... you can simply block (deny) all traffic to and from that computer in your router. The details will depend on the make and model of the router - you could call support at your ISP or the manufacturer for an explanation.

Once blocked the DAW will see the local computers but it won't see the internet.

I want to add a "software" solutions:
1) if you disable/enable the interface the effect is close to unplugging the cable.
2) if you configure the IP for the interface statically, you can remove the Gateway setting. If no other computers/software has "share Internet" features, effectively your computer will "forget" how to connect to the Internet. That is quite some click initially, but once you have done that once you will be able to restore/disable Internet within 20-30 seconds. It is important to assign "right" IP address, otherwise your router can give the same address to another device coursing fancy problems, so that "right" address should be either from the range your router never use or you configure the router to always assigned the same address to this particular computer.
 
Software solutions are more tricky, but hardware solutions (cable, firewall inside router, etc.) have at least one side effect: as soon as Windows "think" it is connected to the Internet, it tries to update/"call home"/sync storage/etc. So it starts some activity. It will fail when blocked on the other end of the wire, but it will try again, and again, and again... I mean it will restart corresponding "service tasks", possibly interfering with the DAW.
F.e. you shortly want transfer some file, connect the cable and Windows immediately start all possible "updaters". Even after you unplug the cable it can take a while till all that programs stop eating resources.